%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU726^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:42 AM UTC 2026
% Result : Theorem 1.73s 1.52s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 106 ( 21 unt; 0 typ; 2 def)
% Number of atoms : 1505 ( 402 equ; 0 cnn)
% Maximal formula atoms : 14 ( 14 avg)
% Number of connectives : 1592 ( 191 ~; 174 |; 101 &;1042 @)
% ( 15 <=>; 69 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 23 con; 0-3 aty)
% Number of variables : 240 ( 0 ^; 186 !; 54 ?; 240 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
powerset: $i > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
setminus: $i > $i > $i ).
thf(func_def_20,type,
sK9: $i > $i > $i > $i ).
thf(f241,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f223,f229,f240]) ).
thf(f240,plain,
~ spl16_10,
inference(avatar_contradiction_clause,[status(thm)],[f239]) ).
thf(f239,plain,
( $false
| ~ spl16_10 ),
inference(subsumption_resolution,[status(thm)],[f238,f61]) ).
thf(f61,plain,
( ( in @ sK8 @ ( powerset @ sK6 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
( ( setminusER = $true )
& ( $true
= ( in @ sK7 @ ( powerset @ sK6 ) ) )
& ( ( subset @ sK7 @ sK8 )
!= $true )
& ( ( in @ sK8 @ ( powerset @ sK6 ) )
= $true )
& ( ( subset @ ( setminus @ sK6 @ sK8 ) @ ( setminus @ sK6 @ sK7 ) )
= $true )
& ( subsetTI = $true )
& ( subsetE = $true )
& ( setminusI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f25,f38,f37]) ).
thf(f37,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( subset @ X1 @ X2 )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= $true ) ) )
=> ( ( $true
= ( in @ sK7 @ ( powerset @ sK6 ) ) )
& ? [X2: $i] :
( ( ( subset @ sK7 @ X2 )
!= $true )
& ( $true
= ( in @ X2 @ ( powerset @ sK6 ) ) )
& ( ( subset @ ( setminus @ sK6 @ X2 ) @ ( setminus @ sK6 @ sK7 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f38,plain,
( ? [X2: $i] :
( ( ( subset @ sK7 @ X2 )
!= $true )
& ( $true
= ( in @ X2 @ ( powerset @ sK6 ) ) )
& ( ( subset @ ( setminus @ sK6 @ X2 ) @ ( setminus @ sK6 @ sK7 ) )
= $true ) )
=> ( ( ( subset @ sK7 @ sK8 )
!= $true )
& ( ( in @ sK8 @ ( powerset @ sK6 ) )
= $true )
& ( ( subset @ ( setminus @ sK6 @ sK8 ) @ ( setminus @ sK6 @ sK7 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f25,plain,
( ( setminusER = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
& ? [X2: $i] :
( ( ( subset @ X1 @ X2 )
!= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
& ( ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= $true ) ) )
& ( subsetTI = $true )
& ( subsetE = $true )
& ( setminusI = $true ) ),
inference(flattening,[status(thm)],[f24]) ).
thf(f24,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ( ( subset @ X1 @ X2 )
!= $true )
& ( ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ ( powerset @ X0 ) )
= $true ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( subsetTI = $true )
& ( setminusER = $true )
& ( setminusI = $true )
& ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( subsetE = $true )
=> ( ( setminusI = $true )
=> ( ( setminusER = $true )
=> ( ( subsetTI = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X0 ) )
= $true )
=> ( ( ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
= $true )
=> ( ( subset @ X1 @ X2 )
= $true ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( subsetE
=> ( setminusI
=> ( setminusER
=> ( subsetTI
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ( ( subset @ ( setminus @ X0 @ X2 ) @ ( setminus @ X0 @ X1 ) )
=> ( subset @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,negated_conjecture,
~ ( subsetE
=> ( setminusI
=> ( setminusER
=> ( subsetTI
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( subset @ ( setminus @ X0 @ X4 ) @ ( setminus @ X0 @ X3 ) )
=> ( subset @ X3 @ X4 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f5,conjecture,
( subsetE
=> ( setminusI
=> ( setminusER
=> ( subsetTI
=> ! [X0: $i,X3: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ( subset @ ( setminus @ X0 @ X4 ) @ ( setminus @ X0 @ X3 ) )
=> ( subset @ X3 @ X4 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OOUkCDmOJm/DTF2THF_24872.p',contrasubsetT3) ).
thf(f238,plain,
( ( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true )
| ~ spl16_10 ),
inference(subsumption_resolution,[status(thm)],[f237,f63]) ).
thf(f63,plain,
( $true
= ( in @ sK7 @ ( powerset @ sK6 ) ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f237,plain,
( ( $true
!= ( in @ sK7 @ ( powerset @ sK6 ) ) )
| ( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true )
| ~ spl16_10 ),
inference(subsumption_resolution,[status(thm)],[f235,f62]) ).
thf(f62,plain,
( ( subset @ sK7 @ sK8 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f235,plain,
( ( ( subset @ sK7 @ sK8 )
= $true )
| ( $true
!= ( in @ sK7 @ ( powerset @ sK6 ) ) )
| ( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true )
| ~ spl16_10 ),
inference(trivial_inequality_removal,[status(thm)],[f233]) ).
thf(f233,plain,
( ( ( in @ sK8 @ ( powerset @ sK6 ) )
!= $true )
| ( $true != $true )
| ( ( subset @ sK7 @ sK8 )
= $true )
| ( $true
!= ( in @ sK7 @ ( powerset @ sK6 ) ) )
| ~ spl16_10 ),
inference(superposition,[status(thm)],[f95,f222]) ).
thf(f222,plain,
( ( ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ sK8 )
= $true )
| ~ spl16_10 ),
inference(avatar_component_clause,[status(thm)],[f220]) ).
thf(f220,definition,
( spl16_10
<=> ( ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl16_10])],[avatar_definition]) ).
thf(f95,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ X0 @ X2 ) )
| ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f71,f59]) ).
thf(f59,plain,
subsetTI = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f71,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ X0 @ X2 ) )
| ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( $true
= ( subset @ X0 @ X2 ) )
| ( ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
& ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X0 )
= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( subsetTI != $true ) )
& ( ( subsetTI = $true )
| ( ( ( in @ sK10 @ ( powerset @ sK11 ) )
= $true )
& ( $true
!= ( subset @ sK10 @ sK12 ) )
& ! [X7: $i] :
( ( ( in @ X7 @ sK12 )
= $true )
| ( $true
!= ( in @ X7 @ sK11 ) )
| ( ( in @ X7 @ sK10 )
!= $true ) )
& ( ( in @ sK12 @ ( powerset @ sK11 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f41,f44,f43,f42]) ).
thf(f42,plain,
! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
=> ( ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X2 )
!= $true )
& ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
& ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f43,plain,
( ? [X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( powerset @ X5 ) ) )
& ? [X6: $i] :
( ( ( subset @ X4 @ X6 )
!= $true )
& ! [X7: $i] :
( ( ( in @ X7 @ X6 )
= $true )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( ( in @ X7 @ X4 )
!= $true ) )
& ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) ) ) )
=> ( ( ( in @ sK10 @ ( powerset @ sK11 ) )
= $true )
& ? [X6: $i] :
( ( $true
!= ( subset @ sK10 @ X6 ) )
& ! [X7: $i] :
( ( ( in @ X7 @ X6 )
= $true )
| ( $true
!= ( in @ X7 @ sK11 ) )
| ( ( in @ X7 @ sK10 )
!= $true ) )
& ( $true
= ( in @ X6 @ ( powerset @ sK11 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f44,plain,
( ? [X6: $i] :
( ( $true
!= ( subset @ sK10 @ X6 ) )
& ! [X7: $i] :
( ( ( in @ X7 @ X6 )
= $true )
| ( $true
!= ( in @ X7 @ sK11 ) )
| ( ( in @ X7 @ sK10 )
!= $true ) )
& ( $true
= ( in @ X6 @ ( powerset @ sK11 ) ) ) )
=> ( ( $true
!= ( subset @ sK10 @ sK12 ) )
& ! [X7: $i] :
( ( ( in @ X7 @ sK12 )
= $true )
| ( $true
!= ( in @ X7 @ sK11 ) )
| ( ( in @ X7 @ sK10 )
!= $true ) )
& ( ( in @ sK12 @ ( powerset @ sK11 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f41,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( $true
= ( subset @ X0 @ X2 ) )
| ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( subsetTI != $true ) )
& ( ( subsetTI = $true )
| ? [X4: $i,X5: $i] :
( ( $true
= ( in @ X4 @ ( powerset @ X5 ) ) )
& ? [X6: $i] :
( ( ( subset @ X4 @ X6 )
!= $true )
& ! [X7: $i] :
( ( ( in @ X7 @ X6 )
= $true )
| ( $true
!= ( in @ X7 @ X5 ) )
| ( ( in @ X7 @ X4 )
!= $true ) )
& ( $true
= ( in @ X6 @ ( powerset @ X5 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f40]) ).
thf(f40,plain,
( ( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( $true
= ( subset @ X0 @ X2 ) )
| ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
| ( subsetTI != $true ) )
& ( ( subsetTI = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
& ? [X2: $i] :
( ( $true
!= ( subset @ X0 @ X2 ) )
& ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
| ( ( in @ X3 @ X1 )
!= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ! [X2: $i] :
( ( $true
= ( subset @ X0 @ X2 ) )
| ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) ) )
<=> ( subsetTI = $true ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
( ! [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( $true
= ( subset @ X0 @ X2 ) )
| ? [X3: $i] :
( ( $true
!= ( in @ X3 @ X2 ) )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true ) )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) )
<=> ( subsetTI = $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( powerset @ X1 ) ) )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X1 ) ) )
=> ( ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ( in @ X3 @ X0 )
= $true )
=> ( $true
= ( in @ X3 @ X2 ) ) ) )
=> ( $true
= ( subset @ X0 @ X2 ) ) ) ) )
<=> ( subsetTI = $true ) ),
inference(fool_elimination,[status(thm)],[f16]) ).
thf(f16,plain,
( subsetTI
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ( ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( in @ X3 @ X0 )
=> ( in @ X3 @ X2 ) ) )
=> ( subset @ X0 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( subsetTI
= ( ! [X3: $i,X0: $i] :
( ( in @ X3 @ ( powerset @ X0 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X0 ) )
=> ( ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( in @ X2 @ X3 )
=> ( in @ X2 @ X4 ) ) )
=> ( subset @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OOUkCDmOJm/DTF2THF_24872.p',subsetTI) ).
thf(f229,plain,
~ spl16_9,
inference(avatar_contradiction_clause,[status(thm)],[f228]) ).
thf(f228,plain,
( $false
| ~ spl16_9 ),
inference(subsumption_resolution,[status(thm)],[f226,f155]) ).
thf(f155,plain,
( $true
= ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ sK7 ) ),
inference(subsumption_resolution,[status(thm)],[f144,f62]) ).
thf(f144,plain,
( ( ( subset @ sK7 @ sK8 )
= $true )
| ( $true
= ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ sK7 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f143]) ).
thf(f143,plain,
( ( $true != $true )
| ( ( subset @ sK7 @ sK8 )
= $true )
| ( $true
= ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ sK7 ) ) ),
inference(superposition,[status(thm)],[f115,f63]) ).
thf(f115,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( powerset @ sK6 ) )
!= $true )
| ( ( subset @ X0 @ sK8 )
= $true )
| ( ( in @ ( sK9 @ sK8 @ sK6 @ X0 ) @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( powerset @ sK6 ) )
!= $true )
| ( ( in @ ( sK9 @ sK8 @ sK6 @ X0 ) @ X0 )
= $true )
| ( $true != $true )
| ( ( subset @ X0 @ sK8 )
= $true ) ),
inference(superposition,[status(thm)],[f97,f61]) ).
thf(f97,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( $true
= ( subset @ X0 @ X2 ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ X0 @ X2 ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f69,f59]) ).
thf(f69,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ X0 @ X2 ) )
| ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X0 )
= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f226,plain,
( ( $true
!= ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ sK7 ) )
| ~ spl16_9 ),
inference(trivial_inequality_removal,[status(thm)],[f224]) ).
thf(f224,plain,
( ( $true != $true )
| ( $true
!= ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ sK7 ) )
| ~ spl16_9 ),
inference(superposition,[status(thm)],[f94,f218]) ).
thf(f218,plain,
( ( $true
= ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK7 ) ) )
| ~ spl16_9 ),
inference(avatar_component_clause,[status(thm)],[f216]) ).
thf(f216,definition,
( spl16_9
<=> ( $true
= ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl16_9])],[avatar_definition]) ).
thf(f94,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( ( in @ X0 @ X2 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f52,f64]) ).
thf(f64,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f52,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ( ( $true
= ( in @ sK0 @ sK2 ) )
& ( ( in @ sK0 @ ( setminus @ sK1 @ sK2 ) )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f30,f31]) ).
thf(f31,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ X5 ) )
& ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
= $true ) )
=> ( ( $true
= ( in @ sK0 @ sK2 ) )
& ( ( in @ sK0 @ ( setminus @ sK1 @ sK2 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ X5 ) )
& ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
=> ( $true
!= ( in @ X0 @ X1 ) ) )
<=> ( setminusER = $true ) ),
inference(flattening,[status(thm)],[f13]) ).
thf(f13,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
=> ( $true
!= ( in @ X0 @ X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f12]) ).
thf(f12,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
=> ~ ( in @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( setminusER
= ( ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OOUkCDmOJm/DTF2THF_24872.p',setminusER) ).
thf(f223,plain,
( spl16_9
| spl16_10 ),
inference(avatar_split_clause,[status(thm)],[f214,f220,f216]) ).
thf(f214,plain,
( ( $true
= ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK7 ) ) )
| ( ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ sK8 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f211]) ).
thf(f211,plain,
( ( $true
= ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ ( setminus @ sK6 @ sK7 ) ) )
| ( $true != $true )
| ( ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ sK8 )
= $true ) ),
inference(superposition,[status(thm)],[f101,f189]) ).
thf(f189,plain,
! [X0: $i] :
( ( ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ ( setminus @ sK6 @ X0 ) )
= $true )
| ( $true
= ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f188]) ).
thf(f188,plain,
! [X0: $i] :
( ( ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ ( setminus @ sK6 @ X0 ) )
= $true )
| ( $true != $true )
| ( $true
= ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ X0 ) ) ),
inference(superposition,[status(thm)],[f99,f177]) ).
thf(f177,plain,
( ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ sK6 )
= $true ),
inference(subsumption_resolution,[status(thm)],[f170,f62]) ).
thf(f170,plain,
( ( ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ sK6 )
= $true )
| ( ( subset @ sK7 @ sK8 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f169]) ).
thf(f169,plain,
( ( $true != $true )
| ( ( in @ ( sK9 @ sK8 @ sK6 @ sK7 ) @ sK6 )
= $true )
| ( ( subset @ sK7 @ sK8 )
= $true ) ),
inference(superposition,[status(thm)],[f119,f63]) ).
thf(f119,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( powerset @ sK6 ) )
!= $true )
| ( ( subset @ X0 @ sK8 )
= $true )
| ( ( in @ ( sK9 @ sK8 @ sK6 @ X0 ) @ sK6 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f116]) ).
thf(f116,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( powerset @ sK6 ) )
!= $true )
| ( $true != $true )
| ( ( subset @ X0 @ sK8 )
= $true )
| ( ( in @ ( sK9 @ sK8 @ sK6 @ X0 ) @ sK6 )
= $true ) ),
inference(superposition,[status(thm)],[f98,f61]) ).
thf(f98,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ X0 @ X2 ) )
| ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true != $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( $true
= ( subset @ X0 @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f70,f59]) ).
thf(f70,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( powerset @ X1 ) ) )
| ( $true
= ( subset @ X0 @ X2 ) )
| ( ( in @ ( sK9 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ ( powerset @ X1 ) ) )
| ( subsetTI != $true ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f99,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( in @ X3 @ X5 ) )
| ( ( in @ X3 @ X4 )
= $true )
| ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( $true
!= ( in @ X3 @ X5 ) )
| ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f72,f57]) ).
thf(f57,plain,
setminusI = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f72,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
!= ( in @ X3 @ X5 ) )
| ( setminusI != $true ) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
thf(f49,plain,
( ( ( setminusI = $true )
| ( ( ( in @ sK13 @ sK14 )
!= $true )
& ( $true
!= ( in @ sK13 @ ( setminus @ sK15 @ sK14 ) ) )
& ( $true
= ( in @ sK13 @ sK15 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
!= ( in @ X3 @ X5 ) ) )
| ( setminusI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f47,f48]) ).
thf(f48,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true )
& ( ( in @ X0 @ X2 )
= $true ) )
=> ( ( ( in @ sK13 @ sK14 )
!= $true )
& ( $true
!= ( in @ sK13 @ ( setminus @ sK15 @ sK14 ) ) )
& ( $true
= ( in @ sK13 @ sK15 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f47,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true )
& ( ( in @ X0 @ X2 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X4 )
= $true )
| ( $true
= ( in @ X3 @ ( setminus @ X5 @ X4 ) ) )
| ( $true
!= ( in @ X3 @ X5 ) ) )
| ( setminusI != $true ) ) ),
inference(rectify,[status(thm)],[f46]) ).
thf(f46,plain,
( ( ( setminusI = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
& ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
!= $true )
& ( $true
= ( in @ X0 @ X1 ) ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) ) )
| ( setminusI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X2 )
= $true )
| ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true )
| ( ( in @ X0 @ X2 )
= $true )
| ( $true
!= ( in @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
( ( setminusI = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( ( in @ X0 @ X2 )
!= $true )
=> ( ( in @ X0 @ ( setminus @ X1 @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,plain,
( setminusI
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( ~ ( in @ X0 @ X2 )
=> ( in @ X0 @ ( setminus @ X1 @ X2 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( setminusI
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ( ~ ( in @ X2 @ X1 )
=> ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.OOUkCDmOJm/DTF2THF_24872.p',setminusI) ).
thf(f101,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setminus @ sK6 @ sK8 ) )
!= $true )
| ( $true
= ( in @ X0 @ ( setminus @ sK6 @ sK7 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setminus @ sK6 @ sK8 ) )
!= $true )
| ( $true
= ( in @ X0 @ ( setminus @ sK6 @ sK7 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f96,f60]) ).
thf(f60,plain,
( ( subset @ ( setminus @ sK6 @ sK8 ) @ ( setminus @ sK6 @ sK7 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f96,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( subset @ X3 @ X5 ) )
| ( ( in @ X4 @ X3 )
!= $true )
| ( $true
= ( in @ X4 @ X5 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
!= ( subset @ X3 @ X5 ) )
| ( $true != $true )
| ( ( in @ X4 @ X3 )
!= $true )
| ( $true
= ( in @ X4 @ X5 ) ) ),
inference(definition_unfolding,[status(thm)],[f53,f58]) ).
thf(f58,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f53,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( $true
= ( in @ X4 @ X5 ) )
| ( $true
!= ( subset @ X3 @ X5 ) )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( subsetE = $true )
| ( ( ( in @ sK4 @ sK3 )
= $true )
& ( ( in @ sK4 @ sK5 )
!= $true )
& ( $true
= ( subset @ sK3 @ sK5 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( $true
= ( in @ X4 @ X5 ) )
| ( $true
!= ( subset @ X3 @ X5 ) ) )
| ( subsetE != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f34,f35]) ).
thf(f35,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( ( in @ X1 @ X2 )
!= $true )
& ( $true
= ( subset @ X0 @ X2 ) ) )
=> ( ( ( in @ sK4 @ sK3 )
= $true )
& ( ( in @ sK4 @ sK5 )
!= $true )
& ( $true
= ( subset @ sK3 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f34,plain,
( ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ( ( in @ X1 @ X2 )
!= $true )
& ( $true
= ( subset @ X0 @ X2 ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( $true
= ( in @ X4 @ X5 ) )
| ( $true
!= ( subset @ X3 @ X5 ) ) )
| ( subsetE != $true ) ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ( subsetE = $true )
| ? [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( ( in @ X2 @ X0 )
!= $true )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( subsetE != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( ( subsetE = $true )
<=> ! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
| ( ( in @ X2 @ X0 )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f26]) ).
thf(f26,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( ( in @ X2 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: $i,X0: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
file('/export/starexec/sandbox2/tmp/tmp.OOUkCDmOJm/DTF2THF_24872.p',subsetE) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU726^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.35 % Computer : n028.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Tue Feb 24 12:32:12 EST 2026
% 0.17/0.36 % CPUTime :
% 0.17/0.36 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU726^2 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.30/0.46 % Version : Especial > Reduced > Especial.
% 0.30/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.30/0.46 % subset (setminus A Y) (setminus A X) -> subset X Y))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC228l [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 13 ( 4 unt; 8 typ; 4 def)
% 0.30/0.46 % Number of atoms : 30 ( 4 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 8 ( 6 avg)
% 0.30/0.46 % Number of connectives : 67 ( 2 ~; 0 |; 0 &; 48 @)
% 0.30/0.46 % ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 15 ( 4 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 9 ( 8 usr; 4 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=286
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(powerset_type,type,
% 0.30/0.46 powerset: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(subset_type,type,
% 0.30/0.46 subset: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE_type,type,
% 0.30/0.46 subsetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetE,definition,
% 0.30/0.46 ( subsetE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( subset @ A @ B )
% 0.30/0.46 => ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminus_type,type,
% 0.30/0.46 setminus: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setminusI_type,type,
% 0.30/0.46 setminusI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusI,definition,
% 0.30/0.46 ( setminusI
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ~ ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setminusER_type,type,
% 0.30/0.46 setminusER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setminusER,definition,
% 0.30/0.46 ( setminusER
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subsetTI_type,type,
% 0.30/0.46 subsetTI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subsetTI,definition,
% 0.30/0.46 ( subsetTI
% 0.30/0.46 = ( ! [A: $i,X: $i] :
% 0.30/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.46 => ! [Y: $i] :
% 0.30/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx @ X )
% 0.30/0.46 => ( in @ Xx @ Y ) ) )
% 0.30/0.46 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(contrasubsetT3,conjecture,
% 0.30/0.46 ( subsetE
% 0.30/0.46 => ( setminusI
% 0.30/0.46 => ( setminusER
% 0.30/0.46 => ( subsetTI
% 0.30/0.46 => ! [A: $i,X: $i] :
% 0.30/0.46 ( ( in @ X @ ( powerset @ A ) )
% 0.30/0.46 => ! [Y: $i] :
% 0.30/0.46 ( ( in @ Y @ ( powerset @ A ) )
% 0.30/0.46 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.30/0.46 => ( subset @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.54/1.39 ---- Embedded in THF ---
% 1.54/1.39 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.39 %%% Generated on Tue Feb 24 12:32:13 EST 2026
% 1.54/1.39 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.39 %%% Logic specification used:
% 1.54/1.39 %%% thf(spec, logic, $$dhol).
% 1.54/1.39
% 1.54/1.39 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.OOUkCDmOJm/DTF2DTF24872.p
% See solution above
% 1.54/1.39 ------------------------
% 1.72/1.40 ---- Cleaned THF ---
% 1.72/1.40 thf(in_type,type,
% 1.72/1.40 in: $i > $i > $o ).
% 1.72/1.40
% 1.72/1.40 thf(powerset_type,type,
% 1.72/1.40 powerset: $i > $i ).
% 1.72/1.40
% 1.72/1.40 thf(subset_type,type,
% 1.72/1.40 subset: $i > $i > $o ).
% 1.72/1.40
% 1.72/1.40 thf(subsetE_type,type,
% 1.72/1.40 subsetE: $o ).
% 1.72/1.40
% 1.72/1.40 thf(subsetE,definition,
% 1.72/1.40 ( subsetE
% 1.72/1.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.72/1.40 ( ( subset @ A @ B )
% 1.72/1.40 => ( ( in @ Xx @ A )
% 1.72/1.40 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.72/1.40
% 1.72/1.40 thf(setminus_type,type,
% 1.72/1.40 setminus: $i > $i > $i ).
% 1.72/1.40
% 1.72/1.40 thf(setminusI_type,type,
% 1.72/1.40 setminusI: $o ).
% 1.72/1.40
% 1.72/1.40 thf(setminusI,definition,
% 1.72/1.40 ( setminusI
% 1.72/1.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.72/1.40 ( ( in @ Xx @ A )
% 1.72/1.40 => ( ~ ( in @ Xx @ B )
% 1.72/1.40 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 1.72/1.40
% 1.72/1.40 thf(setminusER_type,type,
% 1.72/1.40 setminusER: $o ).
% 1.72/1.40
% 1.72/1.40 thf(setminusER,definition,
% 1.72/1.40 ( setminusER
% 1.72/1.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.72/1.40 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 1.72/1.40 => ~ ( in @ Xx @ B ) ) ) ) ).
% 1.72/1.40
% 1.72/1.40 thf(subsetTI_type,type,
% 1.72/1.40 subsetTI: $o ).
% 1.72/1.40
% 1.72/1.40 thf(subsetTI,definition,
% 1.72/1.40 ( subsetTI
% 1.72/1.40 = ( ! [A: $i,X: $i] :
% 1.72/1.40 ( ( in @ X @ ( powerset @ A ) )
% 1.72/1.40 => ! [Y: $i] :
% 1.72/1.40 ( ( in @ Y @ ( powerset @ A ) )
% 1.72/1.40 => ( ! [Xx: $i] :
% 1.72/1.40 ( ( in @ Xx @ A )
% 1.72/1.40 => ( ( in @ Xx @ X )
% 1.72/1.40 => ( in @ Xx @ Y ) ) )
% 1.72/1.40 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 1.72/1.40
% 1.72/1.40 thf(contrasubsetT3,conjecture,
% 1.72/1.40 ( subsetE
% 1.72/1.40 => ( setminusI
% 1.72/1.40 => ( setminusER
% 1.72/1.40 => ( subsetTI
% 1.72/1.40 => ! [A: $i,X: $i] :
% 1.72/1.40 ( ( in @ X @ ( powerset @ A ) )
% 1.72/1.40 => ! [Y: $i] :
% 1.72/1.40 ( ( in @ Y @ ( powerset @ A ) )
% 1.72/1.40 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 1.72/1.40 => ( subset @ X @ Y ) ) ) ) ) ) ) ) ).
% 1.72/1.40 ------------------------
% 1.72/1.42 % (24970)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/183Mi)
% 1.72/1.42 % (24972)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/27Mi)
% 1.72/1.42 % (24973)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/2Mi)
% 1.72/1.42 % (24974)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/2Mi)
% 1.72/1.42 % (24975)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/275Mi)
% 1.72/1.42 % (24976)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/18Mi)
% 1.72/1.42 % (24971)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/4Mi)
% 1.72/1.43 % (24973)Instruction limit reached!
% 1.72/1.43 % (24973)------------------------------
% 1.72/1.43 % (24973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.43 % (24973)Termination reason: Unknown
% 1.72/1.43 % (24974)Instruction limit reached!
% 1.72/1.43 % (24974)------------------------------
% 1.72/1.43 % (24974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.43 % (24973)Termination phase: Property scanning
% 1.72/1.43
% 1.72/1.43 % (24973)Memory used [KB]: 1023
% 1.72/1.43 % (24973)Time elapsed: 0.003 s
% 1.72/1.43 % (24973)Instructions burned: 3 (million)
% 1.72/1.43 % (24973)------------------------------
% 1.72/1.43 % (24973)------------------------------
% 1.72/1.43 % (24974)Termination reason: Unknown
% 1.72/1.43 % (24974)Termination phase: Function definition elimination
% 1.72/1.43
% 1.72/1.43 % (24974)Memory used [KB]: 1023
% 1.72/1.43 % (24974)Time elapsed: 0.003 s
% 1.72/1.43 % (24974)Instructions burned: 3 (million)
% 1.72/1.43 % (24974)------------------------------
% 1.72/1.43 % (24974)------------------------------
% 1.72/1.43 % (24971)Instruction limit reached!
% 1.72/1.43 % (24971)------------------------------
% 1.72/1.43 % (24971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.43 % (24971)Termination reason: Unknown
% 1.72/1.43 % (24971)Termination phase: Saturation
% 1.72/1.43
% 1.72/1.43 % (24971)Memory used [KB]: 5500
% 1.72/1.43 % (24971)Time elapsed: 0.004 s
% 1.72/1.43 % (24971)Instructions burned: 4 (million)
% 1.72/1.43 % (24971)------------------------------
% 1.72/1.43 % (24971)------------------------------
% 1.72/1.43 % (24976)Instruction limit reached!
% 1.72/1.43 % (24976)------------------------------
% 1.72/1.43 % (24976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.43 % (24976)Termination reason: Unknown
% 1.72/1.43 % (24976)Termination phase: Saturation
% 1.72/1.43
% 1.72/1.43 % (24976)Memory used [KB]: 5628
% 1.72/1.43 % (24976)Time elapsed: 0.011 s
% 1.72/1.43 % (24976)Instructions burned: 18 (million)
% 1.72/1.43 % (24976)------------------------------
% 1.72/1.43 % (24976)------------------------------
% 1.72/1.44 % (24972)Instruction limit reached!
% 1.72/1.44 % (24972)------------------------------
% 1.72/1.44 % (24972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.44 % (24972)Termination reason: Unknown
% 1.72/1.44 % (24972)Termination phase: Saturation
% 1.72/1.44
% 1.72/1.44 % (24972)Memory used [KB]: 5628
% 1.72/1.44 % (24972)Time elapsed: 0.016 s
% 1.72/1.44 % (24972)Instructions burned: 28 (million)
% 1.72/1.44 % (24972)------------------------------
% 1.72/1.44 % (24972)------------------------------
% 1.72/1.44 % (24978)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/37Mi)
% 1.72/1.44 % (24979)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/15Mi)
% 1.72/1.44 % (24977)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/3Mi)
% 1.72/1.45 % (24977)Instruction limit reached!
% 1.72/1.45 % (24977)------------------------------
% 1.72/1.45 % (24977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (24977)Termination reason: Unknown
% 1.72/1.45 % (24977)Termination phase: Function definition elimination
% 1.72/1.45
% 1.72/1.45 % (24977)Memory used [KB]: 1023
% 1.72/1.45 % (24977)Time elapsed: 0.003 s
% 1.72/1.45 % (24977)Instructions burned: 3 (million)
% 1.72/1.45 % (24977)------------------------------
% 1.72/1.45 % (24977)------------------------------
% 1.72/1.45 % (24979)Instruction limit reached!
% 1.72/1.45 % (24979)------------------------------
% 1.72/1.45 % (24979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (24979)Termination reason: Unknown
% 1.72/1.45 % (24979)Termination phase: Saturation
% 1.72/1.45
% 1.72/1.45 % (24979)Memory used [KB]: 5628
% 1.72/1.45 % (24979)Time elapsed: 0.010 s
% 1.72/1.45 % (24979)Instructions burned: 16 (million)
% 1.72/1.45 % (24979)------------------------------
% 1.72/1.45 % (24979)------------------------------
% 1.72/1.45 % (24980)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/3Mi)
% 1.72/1.45 % (24981)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/1041Mi)
% 1.72/1.45 % (24980)Instruction limit reached!
% 1.72/1.45 % (24980)------------------------------
% 1.72/1.45 % (24980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.45 % (24980)Termination reason: Unknown
% 1.72/1.45 % (24980)Termination phase: Function definition elimination
% 1.72/1.45
% 1.72/1.45 % (24980)Memory used [KB]: 1023
% 1.72/1.45 % (24980)Time elapsed: 0.003 s
% 1.72/1.45 % (24980)Instructions burned: 3 (million)
% 1.72/1.45 % (24980)------------------------------
% 1.72/1.45 % (24980)------------------------------
% 1.72/1.46 % (24978)Instruction limit reached!
% 1.72/1.46 % (24978)------------------------------
% 1.72/1.46 % (24978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (24978)Termination reason: Unknown
% 1.72/1.46 % (24978)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (24978)Memory used [KB]: 5628
% 1.72/1.46 % (24978)Time elapsed: 0.020 s
% 1.72/1.46 % (24978)Instructions burned: 38 (million)
% 1.72/1.46 % (24978)------------------------------
% 1.72/1.46 % (24978)------------------------------
% 1.72/1.46 % (24982)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/7Mi)
% 1.72/1.46 % (24982)Instruction limit reached!
% 1.72/1.46 % (24982)------------------------------
% 1.72/1.46 % (24982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.46 % (24982)Termination reason: Unknown
% 1.72/1.46 % (24982)Termination phase: Saturation
% 1.72/1.46
% 1.72/1.46 % (24982)Memory used [KB]: 1023
% 1.72/1.46 % (24982)Time elapsed: 0.005 s
% 1.72/1.46 % (24982)Instructions burned: 8 (million)
% 1.72/1.46 % (24982)------------------------------
% 1.72/1.46 % (24982)------------------------------
% 1.72/1.47 % (24983)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/16Mi)
% 1.72/1.47 % (24984)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/3Mi)
% 1.72/1.47 % (24984)Instruction limit reached!
% 1.72/1.47 % (24984)------------------------------
% 1.72/1.47 % (24984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.47 % (24984)Termination reason: Unknown
% 1.72/1.47 % (24984)Termination phase: Twee Goal Transformation
% 1.72/1.47
% 1.72/1.47 % (24984)Memory used [KB]: 1023
% 1.72/1.47 % (24984)Time elapsed: 0.003 s
% 1.72/1.47 % (24984)Instructions burned: 4 (million)
% 1.72/1.47 % (24984)------------------------------
% 1.72/1.47 % (24984)------------------------------
% 1.72/1.47 % (24970)Instruction limit reached!
% 1.72/1.47 % (24970)------------------------------
% 1.72/1.47 % (24970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.47 % (24970)Termination reason: Unknown
% 1.72/1.47 % (24970)Termination phase: Saturation
% 1.72/1.47
% 1.72/1.47 % (24970)Memory used [KB]: 6396
% 1.72/1.47 % (24970)Time elapsed: 0.058 s
% 1.72/1.47 % (24970)Instructions burned: 185 (million)
% 1.72/1.47 % (24970)------------------------------
% 1.72/1.47 % (24970)------------------------------
% 1.72/1.48 % (24985)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/3Mi)
% 1.72/1.48 % (24983)Instruction limit reached!
% 1.72/1.48 % (24983)------------------------------
% 1.72/1.48 % (24983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.48 % (24983)Termination reason: Unknown
% 1.72/1.48 % (24983)Termination phase: Saturation
% 1.72/1.48
% 1.72/1.48 % (24983)Memory used [KB]: 5884
% 1.72/1.48 % (24983)Time elapsed: 0.032 s
% 1.72/1.48 % (24983)Instructions burned: 17 (million)
% 1.72/1.48 % (24983)------------------------------
% 1.72/1.48 % (24983)------------------------------
% 1.72/1.48 % (24985)Instruction limit reached!
% 1.72/1.48 % (24985)------------------------------
% 1.72/1.48 % (24985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.48 % (24985)Termination reason: Unknown
% 1.72/1.48 % (24985)Termination phase: Property scanning
% 1.72/1.48
% 1.72/1.48 % (24985)Memory used [KB]: 1023
% 1.72/1.48 % (24985)Time elapsed: 0.003 s
% 1.72/1.48 % (24985)Instructions burned: 3 (million)
% 1.72/1.48 % (24985)------------------------------
% 1.72/1.48 % (24985)------------------------------
% 1.72/1.48 % (24986)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/7Mi)
% 1.72/1.48 % (24986)Refutation not found, incomplete strategy
% 1.72/1.48 % (24986)------------------------------
% 1.72/1.48 % (24986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.48 % (24986)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.48
% 1.72/1.48
% 1.72/1.48 % (24986)Memory used [KB]: 5500
% 1.72/1.48 % (24986)Time elapsed: 0.026 s
% 1.72/1.48 % (24986)Instructions burned: 5 (million)
% 1.72/1.48 % (24986)------------------------------
% 1.72/1.48 % (24986)------------------------------
% 1.72/1.48 % (24988)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/4Mi)
% 1.72/1.48 % (24988)Instruction limit reached!
% 1.72/1.48 % (24988)------------------------------
% 1.72/1.48 % (24988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.48 % (24988)Termination reason: Unknown
% 1.72/1.48 % (24988)Termination phase: Property scanning
% 1.72/1.48
% 1.72/1.48 % (24988)Memory used [KB]: 1023
% 1.72/1.48 % (24988)Time elapsed: 0.002 s
% 1.72/1.48 % (24988)Instructions burned: 4 (million)
% 1.72/1.48 % (24988)------------------------------
% 1.72/1.48 % (24988)------------------------------
% 1.72/1.49 % (24987)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/3Mi)
% 1.72/1.49 % (24987)Instruction limit reached!
% 1.72/1.49 % (24987)------------------------------
% 1.72/1.49 % (24987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.49 % (24987)Termination reason: Unknown
% 1.72/1.49 % (24987)Termination phase: Saturation
% 1.72/1.49
% 1.72/1.49 % (24987)Memory used [KB]: 5500
% 1.72/1.49 % (24987)Time elapsed: 0.004 s
% 1.72/1.49 % (24987)Instructions burned: 4 (million)
% 1.72/1.49 % (24987)------------------------------
% 1.72/1.49 % (24987)------------------------------
% 1.72/1.49 % (24989)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/18Mi)
% 1.72/1.49 % (24990)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/710Mi)
% 1.72/1.49 % (24992)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/902Mi)
% 1.72/1.50 % (24992)Refutation not found, incomplete strategy
% 1.72/1.50 % (24992)------------------------------
% 1.72/1.50 % (24992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.50 % (24992)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.50
% 1.72/1.50
% 1.72/1.50 % (24992)Memory used [KB]: 5500
% 1.72/1.50 % (24992)Time elapsed: 0.002 s
% 1.72/1.50 % (24992)Instructions burned: 4 (million)
% 1.72/1.50 % (24992)------------------------------
% 1.72/1.50 % (24992)------------------------------
% 1.73/1.50 % (24991)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/6Mi)
% 1.73/1.50 % (24989)Instruction limit reached!
% 1.73/1.50 % (24989)------------------------------
% 1.73/1.50 % (24989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.50 % (24989)Termination reason: Unknown
% 1.73/1.50 % (24989)Termination phase: Saturation
% 1.73/1.50
% 1.73/1.50 % (24989)Memory used [KB]: 5628
% 1.73/1.50 % (24989)Time elapsed: 0.011 s
% 1.73/1.50 % (24989)Instructions burned: 19 (million)
% 1.73/1.50 % (24989)------------------------------
% 1.73/1.50 % (24989)------------------------------
% 1.73/1.50 % (24991)Instruction limit reached!
% 1.73/1.50 % (24991)------------------------------
% 1.73/1.50 % (24991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.50 % (24991)Termination reason: Unknown
% 1.73/1.50 % (24991)Termination phase: Saturation
% 1.73/1.50
% 1.73/1.50 % (24991)Memory used [KB]: 5500
% 1.73/1.50 % (24991)Time elapsed: 0.005 s
% 1.73/1.50 % (24991)Instructions burned: 7 (million)
% 1.73/1.50 % (24991)------------------------------
% 1.73/1.50 % (24991)------------------------------
% 1.73/1.51 % (24993)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/21Mi)
% 1.73/1.51 % (24994)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_24872 for (2999ds/5Mi)
% 1.73/1.51 % (24994)Instruction limit reached!
% 1.73/1.51 % (24994)------------------------------
% 1.73/1.51 % (24994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.51 % (24994)Termination reason: Unknown
% 1.73/1.51 % (24994)Termination phase: Saturation
% 1.73/1.51
% 1.73/1.51 % (24994)Memory used [KB]: 5500
% 1.73/1.51 % (24994)Time elapsed: 0.004 s
% 1.73/1.51 % (24994)Instructions burned: 5 (million)
% 1.73/1.51 % (24994)------------------------------
% 1.73/1.51 % (24994)------------------------------
% 1.73/1.51 % (24990)First to succeed.
% 1.73/1.52 % (24981)Also succeeded, but the first one will report.
% 1.73/1.52 % (24993)Instruction limit reached!
% 1.73/1.52 % (24993)------------------------------
% 1.73/1.52 % (24993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.52 % (24993)Termination reason: Unknown
% 1.73/1.52 % (24993)Termination phase: Saturation
% 1.73/1.52
% 1.73/1.52 % (24993)Memory used [KB]: 5628
% 1.73/1.52 % (24993)Time elapsed: 0.014 s
% 1.73/1.52 % (24993)Instructions burned: 22 (million)
% 1.73/1.52 % (24993)------------------------------
% 1.73/1.52 % (24993)------------------------------
% 1.73/1.52 % (24990)Refutation found. Thanks to Tanya!
% 1.73/1.52 % SZS status Theorem for DTF2THF_24872
% 1.73/1.52 % SZS output start Proof for DTF2THF_24872
% 1.73/1.52 thf(func_def_0, type, in: $i > $i > $o).
% 1.73/1.52 thf(func_def_1, type, powerset: $i > $i).
% 1.73/1.52 thf(func_def_2, type, subset: $i > $i > $o).
% 1.73/1.52 thf(func_def_5, type, setminus: $i > $i > $i).
% 1.73/1.52 thf(func_def_20, type, sK9: $i > $i > $i > $i).
% 1.73/1.52 thf(f241,plain,(
% 1.73/1.52 $false),
% 1.73/1.52 inference(avatar_sat_refutation,[status(thm)],[f223,f229,f240])).
% 1.73/1.52 thf(f240,plain,(
% 1.73/1.52 ~spl16_10),
% 1.73/1.52 inference(avatar_contradiction_clause,[status(thm)],[f239])).
% 1.73/1.52 thf(f239,plain,(
% 1.73/1.52 $false | ~spl16_10),
% 1.73/1.52 inference(subsumption_resolution,[status(thm)],[f238,f61])).
% 1.73/1.52 thf(f61,plain,(
% 1.73/1.52 ((in @ sK8 @ (powerset @ sK6)) = $true)),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f39])).
% 1.73/1.52 thf(f39,plain,(
% 1.73/1.52 (setminusER = $true) & (($true = (in @ sK7 @ (powerset @ sK6))) & (((subset @ sK7 @ sK8) != $true) & ((in @ sK8 @ (powerset @ sK6)) = $true) & ((subset @ (setminus @ sK6 @ sK8) @ (setminus @ sK6 @ sK7)) = $true))) & (subsetTI = $true) & (subsetE = $true) & (setminusI = $true)),
% 1.73/1.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f25,f38,f37])).
% 1.73/1.52 thf(f37,plain,(
% 1.73/1.52 ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((subset @ X1 @ X2) != $true) & ((in @ X2 @ (powerset @ X0)) = $true) & ((subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) = $true))) => (($true = (in @ sK7 @ (powerset @ sK6))) & ? [X2 : $i] : (((subset @ sK7 @ X2) != $true) & ($true = (in @ X2 @ (powerset @ sK6))) & ((subset @ (setminus @ sK6 @ X2) @ (setminus @ sK6 @ sK7)) = $true)))),
% 1.73/1.52 introduced(definition,[],[choice_axiom])).
% 1.73/1.52 thf(f38,plain,(
% 1.73/1.52 ? [X2 : $i] : (((subset @ sK7 @ X2) != $true) & ($true = (in @ X2 @ (powerset @ sK6))) & ((subset @ (setminus @ sK6 @ X2) @ (setminus @ sK6 @ sK7)) = $true)) => (((subset @ sK7 @ sK8) != $true) & ((in @ sK8 @ (powerset @ sK6)) = $true) & ((subset @ (setminus @ sK6 @ sK8) @ (setminus @ sK6 @ sK7)) = $true))),
% 1.73/1.52 introduced(definition,[],[choice_axiom])).
% 1.73/1.52 thf(f25,plain,(
% 1.73/1.52 (setminusER = $true) & ? [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2 : $i] : (((subset @ X1 @ X2) != $true) & ((in @ X2 @ (powerset @ X0)) = $true) & ((subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) = $true))) & (subsetTI = $true) & (subsetE = $true) & (setminusI = $true)),
% 1.73/1.52 inference(flattening,[status(thm)],[f24])).
% 1.73/1.52 thf(f24,plain,(
% 1.73/1.52 (((? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((subset @ X1 @ X2) != $true) & ((subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (subsetTI = $true)) & (setminusER = $true)) & (setminusI = $true)) & (subsetE = $true)),
% 1.73/1.52 inference(ennf_transformation,[status(thm)],[f9])).
% 1.73/1.52 thf(f9,plain,(
% 1.73/1.52 ~((subsetE = $true) => ((setminusI = $true) => ((setminusER = $true) => ((subsetTI = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X0)) = $true) => (((subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) = $true) => ((subset @ X1 @ X2) = $true))))))))),
% 1.73/1.52 inference(fool_elimination,[status(thm)],[f8])).
% 1.73/1.52 thf(f8,plain,(
% 1.73/1.52 ~(subsetE => (setminusI => (setminusER => (subsetTI => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ((subset @ (setminus @ X0 @ X2) @ (setminus @ X0 @ X1)) => (subset @ X1 @ X2))))))))),
% 1.73/1.52 inference(rectify,[status(thm)],[f6])).
% 1.73/1.52 thf(f6,negated_conjecture,(
% 1.73/1.52 ~(subsetE => (setminusI => (setminusER => (subsetTI => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((subset @ (setminus @ X0 @ X4) @ (setminus @ X0 @ X3)) => (subset @ X3 @ X4))))))))),
% 1.73/1.52 inference(negated_conjecture,[status(cth)],[f5])).
% 1.73/1.52 thf(f5,conjecture,(
% 1.73/1.52 subsetE => (setminusI => (setminusER => (subsetTI => ! [X0 : $i,X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => ((subset @ (setminus @ X0 @ X4) @ (setminus @ X0 @ X3)) => (subset @ X3 @ X4)))))))),
% 1.73/1.52 file('/export/starexec/sandbox2/tmp/tmp.OOUkCDmOJm/DTF2THF_24872.p',contrasubsetT3)).
% 1.73/1.52 thf(f238,plain,(
% 1.73/1.52 ((in @ sK8 @ (powerset @ sK6)) != $true) | ~spl16_10),
% 1.73/1.52 inference(subsumption_resolution,[status(thm)],[f237,f63])).
% 1.73/1.52 thf(f63,plain,(
% 1.73/1.52 ($true = (in @ sK7 @ (powerset @ sK6)))),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f39])).
% 1.73/1.52 thf(f237,plain,(
% 1.73/1.52 ($true != (in @ sK7 @ (powerset @ sK6))) | ((in @ sK8 @ (powerset @ sK6)) != $true) | ~spl16_10),
% 1.73/1.52 inference(subsumption_resolution,[status(thm)],[f235,f62])).
% 1.73/1.52 thf(f62,plain,(
% 1.73/1.52 ((subset @ sK7 @ sK8) != $true)),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f39])).
% 1.73/1.52 thf(f235,plain,(
% 1.73/1.52 ((subset @ sK7 @ sK8) = $true) | ($true != (in @ sK7 @ (powerset @ sK6))) | ((in @ sK8 @ (powerset @ sK6)) != $true) | ~spl16_10),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f233])).
% 1.73/1.52 thf(f233,plain,(
% 1.73/1.52 ((in @ sK8 @ (powerset @ sK6)) != $true) | ($true != $true) | ((subset @ sK7 @ sK8) = $true) | ($true != (in @ sK7 @ (powerset @ sK6))) | ~spl16_10),
% 1.73/1.52 inference(superposition,[status(thm)],[f95,f222])).
% 1.73/1.52 thf(f222,plain,(
% 1.73/1.52 ((in @ (sK9 @ sK8 @ sK6 @ sK7) @ sK8) = $true) | ~spl16_10),
% 1.73/1.52 inference(avatar_component_clause,[status(thm)],[f220])).
% 1.73/1.52 thf(f220,definition,(
% 1.73/1.52 spl16_10 <=> ((in @ (sK9 @ sK8 @ sK6 @ sK7) @ sK8) = $true)),
% 1.73/1.52 introduced(definition,[new_symbols(naming,[spl16_10])],[avatar_definition])).
% 1.73/1.52 thf(f95,plain,(
% 1.73/1.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK9 @ X2 @ X1 @ X0) @ X2) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != (in @ X2 @ (powerset @ X1))) | ($true = (subset @ X0 @ X2))) )),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.73/1.52 thf(f83,plain,(
% 1.73/1.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1))) | ($true = (subset @ X0 @ X2)) | ((in @ (sK9 @ X2 @ X1 @ X0) @ X2) != $true) | ($true != $true)) )),
% 1.73/1.52 inference(definition_unfolding,[status(thm)],[f71,f59])).
% 1.73/1.52 thf(f59,plain,(
% 1.73/1.52 (subsetTI = $true)),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f39])).
% 1.73/1.52 thf(f71,plain,(
% 1.73/1.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (subset @ X0 @ X2)) | ((in @ (sK9 @ X2 @ X1 @ X0) @ X2) != $true) | ($true != (in @ X2 @ (powerset @ X1))) | (subsetTI != $true)) )),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f45])).
% 1.73/1.52 thf(f45,plain,(
% 1.73/1.52 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (($true = (subset @ X0 @ X2)) | (((in @ (sK9 @ X2 @ X1 @ X0) @ X2) != $true) & ((in @ (sK9 @ X2 @ X1 @ X0) @ X1) = $true) & ((in @ (sK9 @ X2 @ X1 @ X0) @ X0) = $true)) | ($true != (in @ X2 @ (powerset @ X1))))) | (subsetTI != $true)) & ((subsetTI = $true) | (((in @ sK10 @ (powerset @ sK11)) = $true) & (($true != (subset @ sK10 @ sK12)) & ! [X7 : $i] : (((in @ X7 @ sK12) = $true) | ($true != (in @ X7 @ sK11)) | ((in @ X7 @ sK10) != $true)) & ((in @ sK12 @ (powerset @ sK11)) = $true))))),
% 1.73/1.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f41,f44,f43,f42])).
% 1.73/1.52 thf(f42,plain,(
% 1.73/1.52 ! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true != (in @ X3 @ X2)) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true)) => (((in @ (sK9 @ X2 @ X1 @ X0) @ X2) != $true) & ((in @ (sK9 @ X2 @ X1 @ X0) @ X1) = $true) & ((in @ (sK9 @ X2 @ X1 @ X0) @ X0) = $true)))),
% 1.73/1.52 introduced(definition,[],[choice_axiom])).
% 1.73/1.52 thf(f43,plain,(
% 1.73/1.52 ? [X4 : $i,X5 : $i] : (($true = (in @ X4 @ (powerset @ X5))) & ? [X6 : $i] : (((subset @ X4 @ X6) != $true) & ! [X7 : $i] : (((in @ X7 @ X6) = $true) | ($true != (in @ X7 @ X5)) | ((in @ X7 @ X4) != $true)) & ($true = (in @ X6 @ (powerset @ X5))))) => (((in @ sK10 @ (powerset @ sK11)) = $true) & ? [X6 : $i] : (($true != (subset @ sK10 @ X6)) & ! [X7 : $i] : (((in @ X7 @ X6) = $true) | ($true != (in @ X7 @ sK11)) | ((in @ X7 @ sK10) != $true)) & ($true = (in @ X6 @ (powerset @ sK11)))))),
% 1.73/1.52 introduced(definition,[],[choice_axiom])).
% 1.73/1.52 thf(f44,plain,(
% 1.73/1.52 ? [X6 : $i] : (($true != (subset @ sK10 @ X6)) & ! [X7 : $i] : (((in @ X7 @ X6) = $true) | ($true != (in @ X7 @ sK11)) | ((in @ X7 @ sK10) != $true)) & ($true = (in @ X6 @ (powerset @ sK11)))) => (($true != (subset @ sK10 @ sK12)) & ! [X7 : $i] : (((in @ X7 @ sK12) = $true) | ($true != (in @ X7 @ sK11)) | ((in @ X7 @ sK10) != $true)) & ((in @ sK12 @ (powerset @ sK11)) = $true))),
% 1.73/1.52 introduced(definition,[],[choice_axiom])).
% 1.73/1.52 thf(f41,plain,(
% 1.73/1.52 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (($true = (subset @ X0 @ X2)) | ? [X3 : $i] : (($true != (in @ X3 @ X2)) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true)) | ($true != (in @ X2 @ (powerset @ X1))))) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X4 : $i,X5 : $i] : (($true = (in @ X4 @ (powerset @ X5))) & ? [X6 : $i] : (((subset @ X4 @ X6) != $true) & ! [X7 : $i] : (((in @ X7 @ X6) = $true) | ($true != (in @ X7 @ X5)) | ((in @ X7 @ X4) != $true)) & ($true = (in @ X6 @ (powerset @ X5))))))),
% 1.73/1.52 inference(rectify,[status(thm)],[f40])).
% 1.73/1.52 thf(f40,plain,(
% 1.73/1.52 (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (($true = (subset @ X0 @ X2)) | ? [X3 : $i] : (($true != (in @ X3 @ X2)) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true)) | ($true != (in @ X2 @ (powerset @ X1))))) | (subsetTI != $true)) & ((subsetTI = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2 : $i] : (($true != (subset @ X0 @ X2)) & ! [X3 : $i] : (($true = (in @ X3 @ X2)) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X0) != $true)) & ($true = (in @ X2 @ (powerset @ X1))))))),
% 1.73/1.52 inference(nnf_transformation,[status(thm)],[f21])).
% 1.73/1.52 thf(f21,plain,(
% 1.73/1.52 ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2 : $i] : (($true = (subset @ X0 @ X2)) | ? [X3 : $i] : (($true != (in @ X3 @ X2)) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true)) | ($true != (in @ X2 @ (powerset @ X1))))) <=> (subsetTI = $true)),
% 1.73/1.52 inference(flattening,[status(thm)],[f20])).
% 1.73/1.52 thf(f20,plain,(
% 1.73/1.52 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((($true = (subset @ X0 @ X2)) | ? [X3 : $i] : ((($true != (in @ X3 @ X2)) & ((in @ X3 @ X0) = $true)) & ((in @ X3 @ X1) = $true))) | ($true != (in @ X2 @ (powerset @ X1)))) | ($true != (in @ X0 @ (powerset @ X1)))) <=> (subsetTI = $true)),
% 1.73/1.52 inference(ennf_transformation,[status(thm)],[f17])).
% 1.73/1.52 thf(f17,plain,(
% 1.73/1.52 ! [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X1))) => (! [X3 : $i] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ X0) = $true) => ($true = (in @ X3 @ X2)))) => ($true = (subset @ X0 @ X2))))) <=> (subsetTI = $true)),
% 1.73/1.52 inference(fool_elimination,[status(thm)],[f16])).
% 1.73/1.52 thf(f16,plain,(
% 1.73/1.52 (subsetTI = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (subset @ X0 @ X2)))))),
% 1.73/1.52 inference(rectify,[status(thm)],[f4])).
% 1.73/1.52 thf(f4,axiom,(
% 1.73/1.52 (subsetTI = ! [X3 : $i,X0 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X0)) => (! [X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X3) => (in @ X2 @ X4))) => (subset @ X3 @ X4)))))),
% 1.73/1.52 file('/export/starexec/sandbox2/tmp/tmp.OOUkCDmOJm/DTF2THF_24872.p',subsetTI)).
% 1.73/1.52 thf(f229,plain,(
% 1.73/1.52 ~spl16_9),
% 1.73/1.52 inference(avatar_contradiction_clause,[status(thm)],[f228])).
% 1.73/1.52 thf(f228,plain,(
% 1.73/1.52 $false | ~spl16_9),
% 1.73/1.52 inference(subsumption_resolution,[status(thm)],[f226,f155])).
% 1.73/1.52 thf(f155,plain,(
% 1.73/1.52 ($true = (in @ (sK9 @ sK8 @ sK6 @ sK7) @ sK7))),
% 1.73/1.52 inference(subsumption_resolution,[status(thm)],[f144,f62])).
% 1.73/1.52 thf(f144,plain,(
% 1.73/1.52 ((subset @ sK7 @ sK8) = $true) | ($true = (in @ (sK9 @ sK8 @ sK6 @ sK7) @ sK7))),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f143])).
% 1.73/1.52 thf(f143,plain,(
% 1.73/1.52 ($true != $true) | ((subset @ sK7 @ sK8) = $true) | ($true = (in @ (sK9 @ sK8 @ sK6 @ sK7) @ sK7))),
% 1.73/1.52 inference(superposition,[status(thm)],[f115,f63])).
% 1.73/1.52 thf(f115,plain,(
% 1.73/1.52 ( ! [X0 : $i] : (((in @ X0 @ (powerset @ sK6)) != $true) | ((subset @ X0 @ sK8) = $true) | ((in @ (sK9 @ sK8 @ sK6 @ X0) @ X0) = $true)) )),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.73/1.52 thf(f112,plain,(
% 1.73/1.52 ( ! [X0 : $i] : (((in @ X0 @ (powerset @ sK6)) != $true) | ((in @ (sK9 @ sK8 @ sK6 @ X0) @ X0) = $true) | ($true != $true) | ((subset @ X0 @ sK8) = $true)) )),
% 1.73/1.52 inference(superposition,[status(thm)],[f97,f61])).
% 1.73/1.52 thf(f97,plain,(
% 1.73/1.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ((in @ (sK9 @ X2 @ X1 @ X0) @ X0) = $true) | ($true = (subset @ X0 @ X2)) | ($true != (in @ X0 @ (powerset @ X1)))) )),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.73/1.52 thf(f85,plain,(
% 1.73/1.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ((in @ (sK9 @ X2 @ X1 @ X0) @ X0) = $true) | ($true != (in @ X0 @ (powerset @ X1))) | ($true = (subset @ X0 @ X2)) | ($true != $true)) )),
% 1.73/1.52 inference(definition_unfolding,[status(thm)],[f69,f59])).
% 1.73/1.52 thf(f69,plain,(
% 1.73/1.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (subset @ X0 @ X2)) | ((in @ (sK9 @ X2 @ X1 @ X0) @ X0) = $true) | ($true != (in @ X2 @ (powerset @ X1))) | (subsetTI != $true)) )),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f45])).
% 1.73/1.52 thf(f226,plain,(
% 1.73/1.52 ($true != (in @ (sK9 @ sK8 @ sK6 @ sK7) @ sK7)) | ~spl16_9),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f224])).
% 1.73/1.52 thf(f224,plain,(
% 1.73/1.52 ($true != $true) | ($true != (in @ (sK9 @ sK8 @ sK6 @ sK7) @ sK7)) | ~spl16_9),
% 1.73/1.52 inference(superposition,[status(thm)],[f94,f218])).
% 1.73/1.52 thf(f218,plain,(
% 1.73/1.52 ($true = (in @ (sK9 @ sK8 @ sK6 @ sK7) @ (setminus @ sK6 @ sK7))) | ~spl16_9),
% 1.73/1.52 inference(avatar_component_clause,[status(thm)],[f216])).
% 1.73/1.52 thf(f216,definition,(
% 1.73/1.52 spl16_9 <=> ($true = (in @ (sK9 @ sK8 @ sK6 @ sK7) @ (setminus @ sK6 @ sK7)))),
% 1.73/1.52 introduced(definition,[new_symbols(naming,[spl16_9])],[avatar_definition])).
% 1.73/1.52 thf(f94,plain,(
% 1.73/1.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) | ((in @ X0 @ X2) != $true)) )),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.73/1.52 thf(f76,plain,(
% 1.73/1.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) | ((in @ X0 @ X2) != $true) | ($true != $true)) )),
% 1.73/1.52 inference(definition_unfolding,[status(thm)],[f52,f64])).
% 1.73/1.52 thf(f64,plain,(
% 1.73/1.52 (setminusER = $true)),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f39])).
% 1.73/1.52 thf(f52,plain,(
% 1.73/1.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ (setminus @ X1 @ X2)) != $true) | (setminusER != $true)) )),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f32])).
% 1.73/1.52 thf(f32,plain,(
% 1.73/1.52 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ (setminus @ X1 @ X2)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | (($true = (in @ sK0 @ sK2)) & ((in @ sK0 @ (setminus @ sK1 @ sK2)) = $true)))),
% 1.73/1.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f30,f31])).
% 1.73/1.52 thf(f31,plain,(
% 1.73/1.52 ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X3 @ X5)) & ((in @ X3 @ (setminus @ X4 @ X5)) = $true)) => (($true = (in @ sK0 @ sK2)) & ((in @ sK0 @ (setminus @ sK1 @ sK2)) = $true))),
% 1.73/1.52 introduced(definition,[],[choice_axiom])).
% 1.73/1.52 thf(f30,plain,(
% 1.73/1.52 (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X2) != $true) | ((in @ X0 @ (setminus @ X1 @ X2)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X3 @ X5)) & ((in @ X3 @ (setminus @ X4 @ X5)) = $true)))),
% 1.73/1.52 inference(rectify,[status(thm)],[f29])).
% 1.73/1.52 thf(f29,plain,(
% 1.73/1.52 (! [X0 : $i,X2 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ((in @ X0 @ (setminus @ X2 @ X1)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (($true = (in @ X0 @ X1)) & ((in @ X0 @ (setminus @ X2 @ X1)) = $true)))),
% 1.73/1.52 inference(nnf_transformation,[status(thm)],[f28])).
% 1.73/1.52 thf(f28,plain,(
% 1.73/1.52 ! [X0 : $i,X2 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ((in @ X0 @ (setminus @ X2 @ X1)) != $true)) <=> (setminusER = $true)),
% 1.73/1.52 inference(ennf_transformation,[status(thm)],[f18])).
% 1.73/1.52 thf(f18,plain,(
% 1.73/1.52 ! [X1 : $i,X0 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X2 @ X1)) = $true) => ($true != (in @ X0 @ X1))) <=> (setminusER = $true)),
% 1.73/1.52 inference(flattening,[status(thm)],[f13])).
% 1.73/1.52 thf(f13,plain,(
% 1.73/1.52 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setminus @ X2 @ X1)) = $true) => ~($true = (in @ X0 @ X1)))),
% 1.73/1.52 inference(fool_elimination,[status(thm)],[f12])).
% 1.73/1.52 thf(f12,plain,(
% 1.73/1.52 (setminusER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X2 @ X1)) => ~(in @ X0 @ X1)))),
% 1.73/1.52 inference(rectify,[status(thm)],[f3])).
% 1.73/1.52 thf(f3,axiom,(
% 1.73/1.52 (setminusER = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 1.73/1.52 file('/export/starexec/sandbox2/tmp/tmp.OOUkCDmOJm/DTF2THF_24872.p',setminusER)).
% 1.73/1.52 thf(f223,plain,(
% 1.73/1.52 spl16_9 | spl16_10),
% 1.73/1.52 inference(avatar_split_clause,[status(thm)],[f214,f220,f216])).
% 1.73/1.52 thf(f214,plain,(
% 1.73/1.52 ($true = (in @ (sK9 @ sK8 @ sK6 @ sK7) @ (setminus @ sK6 @ sK7))) | ((in @ (sK9 @ sK8 @ sK6 @ sK7) @ sK8) = $true)),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f211])).
% 1.73/1.52 thf(f211,plain,(
% 1.73/1.52 ($true = (in @ (sK9 @ sK8 @ sK6 @ sK7) @ (setminus @ sK6 @ sK7))) | ($true != $true) | ((in @ (sK9 @ sK8 @ sK6 @ sK7) @ sK8) = $true)),
% 1.73/1.52 inference(superposition,[status(thm)],[f101,f189])).
% 1.73/1.52 thf(f189,plain,(
% 1.73/1.52 ( ! [X0 : $i] : (((in @ (sK9 @ sK8 @ sK6 @ sK7) @ (setminus @ sK6 @ X0)) = $true) | ($true = (in @ (sK9 @ sK8 @ sK6 @ sK7) @ X0))) )),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f188])).
% 1.73/1.52 thf(f188,plain,(
% 1.73/1.52 ( ! [X0 : $i] : (((in @ (sK9 @ sK8 @ sK6 @ sK7) @ (setminus @ sK6 @ X0)) = $true) | ($true != $true) | ($true = (in @ (sK9 @ sK8 @ sK6 @ sK7) @ X0))) )),
% 1.73/1.52 inference(superposition,[status(thm)],[f99,f177])).
% 1.73/1.52 thf(f177,plain,(
% 1.73/1.52 ((in @ (sK9 @ sK8 @ sK6 @ sK7) @ sK6) = $true)),
% 1.73/1.52 inference(subsumption_resolution,[status(thm)],[f170,f62])).
% 1.73/1.52 thf(f170,plain,(
% 1.73/1.52 ((in @ (sK9 @ sK8 @ sK6 @ sK7) @ sK6) = $true) | ((subset @ sK7 @ sK8) = $true)),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f169])).
% 1.73/1.52 thf(f169,plain,(
% 1.73/1.52 ($true != $true) | ((in @ (sK9 @ sK8 @ sK6 @ sK7) @ sK6) = $true) | ((subset @ sK7 @ sK8) = $true)),
% 1.73/1.52 inference(superposition,[status(thm)],[f119,f63])).
% 1.73/1.52 thf(f119,plain,(
% 1.73/1.52 ( ! [X0 : $i] : (((in @ X0 @ (powerset @ sK6)) != $true) | ((subset @ X0 @ sK8) = $true) | ((in @ (sK9 @ sK8 @ sK6 @ X0) @ sK6) = $true)) )),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.73/1.52 thf(f116,plain,(
% 1.73/1.52 ( ! [X0 : $i] : (((in @ X0 @ (powerset @ sK6)) != $true) | ($true != $true) | ((subset @ X0 @ sK8) = $true) | ((in @ (sK9 @ sK8 @ sK6 @ X0) @ sK6) = $true)) )),
% 1.73/1.52 inference(superposition,[status(thm)],[f98,f61])).
% 1.73/1.52 thf(f98,plain,(
% 1.73/1.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ (powerset @ X1))) | ($true != (in @ X0 @ (powerset @ X1))) | ($true = (subset @ X0 @ X2)) | ((in @ (sK9 @ X2 @ X1 @ X0) @ X1) = $true)) )),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.73/1.52 thf(f84,plain,(
% 1.73/1.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true != $true) | ($true != (in @ X2 @ (powerset @ X1))) | ((in @ (sK9 @ X2 @ X1 @ X0) @ X1) = $true) | ($true = (subset @ X0 @ X2))) )),
% 1.73/1.52 inference(definition_unfolding,[status(thm)],[f70,f59])).
% 1.73/1.52 thf(f70,plain,(
% 1.73/1.52 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ($true = (subset @ X0 @ X2)) | ((in @ (sK9 @ X2 @ X1 @ X0) @ X1) = $true) | ($true != (in @ X2 @ (powerset @ X1))) | (subsetTI != $true)) )),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f45])).
% 1.73/1.52 thf(f99,plain,(
% 1.73/1.52 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ X5)) | ((in @ X3 @ X4) = $true) | ($true = (in @ X3 @ (setminus @ X5 @ X4)))) )),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.73/1.52 thf(f93,plain,(
% 1.73/1.52 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ($true != (in @ X3 @ X5)) | ($true = (in @ X3 @ (setminus @ X5 @ X4))) | ($true != $true)) )),
% 1.73/1.52 inference(definition_unfolding,[status(thm)],[f72,f57])).
% 1.73/1.52 thf(f57,plain,(
% 1.73/1.52 (setminusI = $true)),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f39])).
% 1.73/1.52 thf(f72,plain,(
% 1.73/1.52 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ($true = (in @ X3 @ (setminus @ X5 @ X4))) | ($true != (in @ X3 @ X5)) | (setminusI != $true)) )),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f49])).
% 1.73/1.52 thf(f49,plain,(
% 1.73/1.52 ((setminusI = $true) | (((in @ sK13 @ sK14) != $true) & ($true != (in @ sK13 @ (setminus @ sK15 @ sK14))) & ($true = (in @ sK13 @ sK15)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ($true = (in @ X3 @ (setminus @ X5 @ X4))) | ($true != (in @ X3 @ X5))) | (setminusI != $true))),
% 1.73/1.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f47,f48])).
% 1.73/1.52 thf(f48,plain,(
% 1.73/1.52 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) & ((in @ X0 @ (setminus @ X2 @ X1)) != $true) & ((in @ X0 @ X2) = $true)) => (((in @ sK13 @ sK14) != $true) & ($true != (in @ sK13 @ (setminus @ sK15 @ sK14))) & ($true = (in @ sK13 @ sK15)))),
% 1.73/1.52 introduced(definition,[],[choice_axiom])).
% 1.73/1.52 thf(f47,plain,(
% 1.73/1.52 ((setminusI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X1)) & ((in @ X0 @ (setminus @ X2 @ X1)) != $true) & ((in @ X0 @ X2) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) = $true) | ($true = (in @ X3 @ (setminus @ X5 @ X4))) | ($true != (in @ X3 @ X5))) | (setminusI != $true))),
% 1.73/1.52 inference(rectify,[status(thm)],[f46])).
% 1.73/1.52 thf(f46,plain,(
% 1.73/1.52 ((setminusI = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ (setminus @ X1 @ X2)) != $true) & ($true = (in @ X0 @ X1)))) & (! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X0 @ X2) = $true) | ((in @ X0 @ (setminus @ X1 @ X2)) = $true) | ($true != (in @ X0 @ X1))) | (setminusI != $true))),
% 1.73/1.52 inference(nnf_transformation,[status(thm)],[f23])).
% 1.73/1.52 thf(f23,plain,(
% 1.73/1.52 (setminusI = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((in @ X0 @ X2) = $true) | ((in @ X0 @ (setminus @ X1 @ X2)) = $true) | ($true != (in @ X0 @ X1)))),
% 1.73/1.52 inference(flattening,[status(thm)],[f22])).
% 1.73/1.52 thf(f22,plain,(
% 1.73/1.52 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setminus @ X1 @ X2)) = $true) | ((in @ X0 @ X2) = $true)) | ($true != (in @ X0 @ X1)))),
% 1.73/1.52 inference(ennf_transformation,[status(thm)],[f19])).
% 1.73/1.52 thf(f19,plain,(
% 1.73/1.52 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) => (((in @ X0 @ X2) != $true) => ((in @ X0 @ (setminus @ X1 @ X2)) = $true)))),
% 1.73/1.52 inference(flattening,[status(thm)],[f11])).
% 1.73/1.52 thf(f11,plain,(
% 1.73/1.52 (setminusI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X1)) => (~((in @ X0 @ X2) = $true) => ((in @ X0 @ (setminus @ X1 @ X2)) = $true)))),
% 1.73/1.52 inference(fool_elimination,[status(thm)],[f10])).
% 1.73/1.52 thf(f10,plain,(
% 1.73/1.52 (setminusI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (~(in @ X0 @ X2) => (in @ X0 @ (setminus @ X1 @ X2)))))),
% 1.73/1.52 inference(rectify,[status(thm)],[f2])).
% 1.73/1.52 thf(f2,axiom,(
% 1.73/1.52 (setminusI = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))))),
% 1.73/1.52 file('/export/starexec/sandbox2/tmp/tmp.OOUkCDmOJm/DTF2THF_24872.p',setminusI)).
% 1.73/1.52 thf(f101,plain,(
% 1.73/1.52 ( ! [X0 : $i] : (((in @ X0 @ (setminus @ sK6 @ sK8)) != $true) | ($true = (in @ X0 @ (setminus @ sK6 @ sK7)))) )),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.73/1.52 thf(f100,plain,(
% 1.73/1.52 ( ! [X0 : $i] : (((in @ X0 @ (setminus @ sK6 @ sK8)) != $true) | ($true = (in @ X0 @ (setminus @ sK6 @ sK7))) | ($true != $true)) )),
% 1.73/1.52 inference(superposition,[status(thm)],[f96,f60])).
% 1.73/1.52 thf(f60,plain,(
% 1.73/1.52 ((subset @ (setminus @ sK6 @ sK8) @ (setminus @ sK6 @ sK7)) = $true)),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f39])).
% 1.73/1.52 thf(f96,plain,(
% 1.73/1.52 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (subset @ X3 @ X5)) | ((in @ X4 @ X3) != $true) | ($true = (in @ X4 @ X5))) )),
% 1.73/1.52 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.73/1.52 thf(f82,plain,(
% 1.73/1.52 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (subset @ X3 @ X5)) | ($true != $true) | ((in @ X4 @ X3) != $true) | ($true = (in @ X4 @ X5))) )),
% 1.73/1.52 inference(definition_unfolding,[status(thm)],[f53,f58])).
% 1.73/1.52 thf(f58,plain,(
% 1.73/1.52 (subsetE = $true)),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f39])).
% 1.73/1.52 thf(f53,plain,(
% 1.73/1.52 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) != $true) | ($true = (in @ X4 @ X5)) | ($true != (subset @ X3 @ X5)) | (subsetE != $true)) )),
% 1.73/1.52 inference(cnf_transformation,[status(thm)],[f36])).
% 1.73/1.52 thf(f36,plain,(
% 1.73/1.52 ((subsetE = $true) | (((in @ sK4 @ sK3) = $true) & ((in @ sK4 @ sK5) != $true) & ($true = (subset @ sK3 @ sK5)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) != $true) | ($true = (in @ X4 @ X5)) | ($true != (subset @ X3 @ X5))) | (subsetE != $true))),
% 1.73/1.52 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f34,f35])).
% 1.73/1.52 thf(f35,plain,(
% 1.73/1.52 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) & ((in @ X1 @ X2) != $true) & ($true = (subset @ X0 @ X2))) => (((in @ sK4 @ sK3) = $true) & ((in @ sK4 @ sK5) != $true) & ($true = (subset @ sK3 @ sK5)))),
% 1.73/1.52 introduced(definition,[],[choice_axiom])).
% 1.73/1.52 thf(f34,plain,(
% 1.73/1.52 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) & ((in @ X1 @ X2) != $true) & ($true = (subset @ X0 @ X2)))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) != $true) | ($true = (in @ X4 @ X5)) | ($true != (subset @ X3 @ X5))) | (subsetE != $true))),
% 1.73/1.52 inference(rectify,[status(thm)],[f33])).
% 1.73/1.52 thf(f33,plain,(
% 1.73/1.52 ((subsetE = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true) & ((subset @ X1 @ X0) = $true))) & (! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true) | ((subset @ X1 @ X0) != $true)) | (subsetE != $true))),
% 1.73/1.52 inference(nnf_transformation,[status(thm)],[f27])).
% 1.73/1.52 thf(f27,plain,(
% 1.73/1.52 (subsetE = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true) | ((subset @ X1 @ X0) != $true))),
% 1.73/1.52 inference(flattening,[status(thm)],[f26])).
% 1.73/1.52 thf(f26,plain,(
% 1.73/1.52 (subsetE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) != $true)) | ((subset @ X1 @ X0) != $true))),
% 1.73/1.52 inference(ennf_transformation,[status(thm)],[f15])).
% 1.73/1.52 thf(f15,plain,(
% 1.73/1.52 (subsetE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) => (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)))),
% 1.73/1.52 inference(fool_elimination,[status(thm)],[f14])).
% 1.73/1.52 thf(f14,plain,(
% 1.73/1.52 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = subsetE)),
% 1.73/1.52 inference(rectify,[status(thm)],[f1])).
% 1.73/1.52 thf(f1,axiom,(
% 1.73/1.52 (! [X1 : $i,X0 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.73/1.52 file('/export/starexec/sandbox2/tmp/tmp.OOUkCDmOJm/DTF2THF_24872.p',subsetE)).
% 1.73/1.52 % SZS output end Proof for DTF2THF_24872
% 1.73/1.52 % (24990)------------------------------
% 1.73/1.52 % (24990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.52 % (24990)Termination reason: Refutation
% 1.73/1.52
% 1.73/1.52 % (24990)Memory used [KB]: 5756
% 1.73/1.52 % (24990)Time elapsed: 0.025 s
% 1.73/1.52 % (24990)Instructions burned: 36 (million)
% 1.73/1.52 % (24990)------------------------------
% 1.73/1.52 % (24990)------------------------------
% 1.73/1.52 % (24969)Success in time 0.109 s
%------------------------------------------------------------------------------